Question

Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?distribute –4 to get –8x 4 > 5 – 3x.distribute –4 to get –8x – 1 > 5 – 3x.subtract 2x from both sides of the inequality.add 1 to both sides of the inequality.

Answer 1

Answer:

Option A is correct.

The first step in solving the inequality is:

to distribute -4 to get  $-8x + 4> 5-3x$

Step-by-step explanation:

The distributive property says that:

$a\cdot(b+c) =a\cdot b + a\cdot c$

Given the inequality:

$-4(2x-1)> 5-3x$

Apply the distributive property we have;

$-4 \cdot (2x) -4\cdot (-1)> 5-3x$

Simplify:

$-8x + 4> 5-3x$

Therefore, the first step in solving the inequality is:

to distribute -4 to get  $-8x + 4> 5-3x$

Answer 2

Distribute –4 to get –8x + 4 > 5 – 3x.

Further explanation

The inequality –4(2x – 1) > 5 – 3x.

We will solve the problem of inequality of one variable. Here are the steps:

Step-1: Distribute –4 to get –8x + 4 > 5 – 3x.

–4(2x – 1) > 5 – 3x

-4(2x) + (-4)(-1) > 5 – 3x

-8x + 4 > 5 – 3x

Therefore, a correct first step in solving the inequality: Distribute –4 to get –8x + 4 > 5 – 3x.

Step-2: Subtract 4 from both sides of the inequality

-8x + 4 - 4 > 5 - 4 – 3x

-8x > 1 – 3x

Step-3: Add 3x from both sides of the inequality

-8x + 3x > 1 – 3x + 3x

-5x > 1

Step-4: Divide -5 from both sides of the inequality

$\boxed{ \ \frac{-5x}{-5} > \frac{1}{-5} \ }$

Thus, the solution is  $\boxed{\boxed{ \ x < -\frac{1}{5} \ }}$

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Notes:

• The Distributive Property:  $\boxed{ \ A(B + C) = A \cdot B + A \cdot C \ }$ or $\boxed{ \ A(B - C) = A \cdot B - A \cdot C \ }$
• If inequality is multiplied or divided by a negative number, then the sign of the inequality changes.

Learn more

1. Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38?  brainly.com/question/1626676  
2. Which is the graph of 2x – 4y > 6 brainly.com/question/4408289#
3. Which table represents a linear function brainly.com/question/10570936

Keywords: a correct first step, in solving the inequality, one variable, distribute, add, subtract, divide, multiply, sign, minus, negative, solution, distributive property